The present invention generally concerns means for generating binary sequences approximating a sine function and more particularly means for generating binary sequences having spectra whose line amplitudes up to a given harmonic order have zero values.
These binary sequences will be called in the following anharmonic sequences since their first, second . . . k.sup.th (k being selected at will) harmonics are equal to zero.
Let us consider a sequence of N non return to zero binary digits, the duration of the digits being 1/f and the duration T of the sequence being ##EQU1## AND LET US DESIGNATE BY S.sub.I THE BINARY VALUE OF THE I.sup.TH DIGIT OF THE SEQUENCE (0 .ltoreq. I .ltoreq. N-1).
The sequence can be expanded into a Fourier series: ##EQU2## WHERE J= .sqroot.-1 AND THE AMPLITUDE OF THE SPECTRUM LINE OF ORDER K S(kF) is given by: ##EQU3## The first factor in the second side of equation (1) is typically a sin x/x digital waveform signal which vanishes when the order k of the harmonic is equal to the number of bits N of the sequence or a multiple of this number whichever be the selected sequence. The second term in this second side ##EQU4## denotes the sum of N complex numbers of modulus 0 or 1.
Sequences can be selected in such a way that the amplitude of a harmonic of predetermined order k vanishes. As indicated in the foregoing, it will be said that such a sequence is anharmonic at said predetermined order or orders.
The method for defining these anharmonic sequences is apparently new and will be detailed in two sections according to the approach involved.